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4/2/2018 1
D.P.Bhaskar, Sanjivani COE Kopargaon
Give FEEDBACK: dpbhaskar@rediffmail.com

1. Lathe
2. Shaping
3. Milling
4. Drilling
Multi-speed Gear Box of Machine Tool
Single input speed (Motor speed) = nem
Multi-Speeds on Spindle shaft (Spindle Speeds)
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n1 ,n2 ,n3 ,n4
n5 ,n6 ,n7 , nz
The extreme spindle speeds
n1 = nmin
nZ = nmax

Why Multi-Speeds ?
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Different :
• Feeds
• W/P Materials
• W/P Dimensions [D]
• Cutting tool materials
n1
n2
n3
n4
n5
n6
n7
n8
N9= nz
nem
1
1

Speed Regulations
Stepped Regulations Stepples Regulations
Discrete speed steps Continuous speed steps
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n1
n2
n3
n4
n5
nz
nem

Why Progressions *To find different speed steps
*Find relation of two speed steps
1. Arithmetic progression (AP)
2. Geometric Progression (GP)
3. Harmonic Progression (HP)
Progression Laws
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Types of Progression Laws

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Difference between 2 successive speeds is constant = at
at= (n2 – n1)= (n3– n2)= (n4 – n3)= (nz– nz-1)
Z=Total speed steps (speeds) on spindle.
(n1, n2, n3, n4,……………………….., nz-1,nz..)
LAW
Ration of 2 successive Speeds= Ø=Speed Ratio

nmax =Maximum spindle speed (rpm)= nz
nmin= Minimum spindle speed (rpm)= n1
n1 =nmin
n2 =n1 + at
n3 = n2 + at =n1 + 2at
n4 = n3 + at =n1 + 3at
nz = n(z-1) + at =n1 + (z-1)at
Dk = Diameters to be Machined at Specific cutting speed (v)
=Upper limit of Diameter
∆Dk = Diameters Range = (D2-D1)
= (D3-D2) ………
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AP
Maximum spindle speed (rpm), nmax =445 rpm
Minimum spindle speed (rpm), nmin=35 rpm
Number of speed steps, Z=12
Cutting speed, v=20 m/min.
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9
D.P.Bhaskar,
Sanjivani COE
Kopargaon
Arithmetic progression

Remarks @ AP
4/2/2018 11
At high spindle speeds, the diameter range is very narrow and hence some of the
speed steps are redundant.
At low spindle speeds the diameter range is wide hence needs to
add more speed steps between calculated values.

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GP
Geometric progression

Range Ratio
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Geometric Progression Ratio
Speed Ratio

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Progression ratio/ Speed ratio
Geometric progression (also inaccurately known as a geometric
series) is a sequence of speeds such that the ratio of any two
successive speeds of the sequence is a constant called the Geometric
progression ratio (speed ratio) of the sequence.
Range ratio
It ratio of maximum and minimum speed

GP
Maximum spindle speed (rpm), nmax =445 rpm
Minimum spindle speed (rpm), nmin=35 rpm
Number of speed steps, Z=12
Cutting speed, v=20 m/min.
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Remarks @ AP
4/2/2018 18
At high spindle speeds, the diameter range is very
narrow and hence some of the speed steps are
redundant.
At low spindle speeds the diameter range is wide
hence needs to add more speed steps between
calculated values.

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Variation in
Diameters is wide
in AP than GP
AP
or
GP?
GP gives Optimum
Distribution Of Gear
Speeds compared to
AP

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Effect of GP ratio

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In gearbox design a set of preferred step ratio or preferred
numbers is used to obtain the series of output speed of
gearbox. The preferred step ratio is mentioned as basic series
named as R5, R10,R20,R40 and R80. Each basic series has a
specific step ratio. R [Charles Renard]
Definition of preferred number/speed series

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Structural Formula
Structural Diagram
Ray Diagram
Speed chart
Gearing Diagram1
2
3
4
5Sequence

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Z =P1(x1)*P2(x2)*....Pu(xu)
Structural Formula
The maximum number of speed that can be obtained from
two shafts is three. Hence its necessary to
use intermediate shafts between the input shaft and output
shaft. The structural formula helps to arrive the number of
stages and required gears to obtain the desired speeds.
Structural Formula
P : Speed steps/ Pairs in any stage
X : Characteristic in stage

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HL=Z=6
VL=N+1=3

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1) MAX Node addition=7.5
2) P of Stage one should be less
BEST
RULE

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BEST

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Z=12
For More than 2 stages 1st and last stage P should be less
BEST
RULE

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Optimum SF

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A ray diagram is a representation of structural
formula. It provides information such as speed in
each stage, the transmission ratio in each stage, The
total number of speeds and its values.
Definition

Ray diagram for Z=4
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RULE
Ray Diagram Speed chart

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Ray Diagram
Kinematic/Gearing Layout
A kinematic layout is a pictorial representation
of a gearbox, describing the arrangement of
gears. It provides information like number of
stages, number of shafts used, number of gear
pairs and its arrangement.
Definition

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RULE

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Gearing Diagram

Z=12
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Gearing Diagram

Number of Teeth and Speed deviation diagram
Write best Structural formula, Draw Structural
Diagram, Ray Diagram, Speed Chart, Gearing
Diagram, No of teeth, Speed Deviation Diagram
Question

Sppeds n1 n2 n3 n4 n5 6
Calculated 100 158 252.8 395 632 995.4
Round off 100 160 250 400 630 1000
e
Ray Diagram, Speed Chart Gearing Diagram
Spindle speeds

Stage 1 No. Of Teeth Calculation
Ray Diagram

No deviation in speeds in stage 1
ZA=20 ZA’=50 GA=2.5
ZB=27 ZB’=43 GB=1.59
C1=70

Ray Diagram

Deviation in speeds in stage 2
ZC=20 ZC’=80 GE=4
ZD=38 ZD’=61 GD=1.631
ZE=61 ZE’=39 GC=0.639
C2=100

GE=4
GD=1.6
GC=0.635
GE=4
GD=1.631
GC=0.639
𝐺𝐷 =
𝑛𝐷
𝑛𝐷′
𝑛𝐷′ = 𝑛𝐷/GD=400/1.635=244.64
𝑛𝐷′ = 𝑛𝐷/GD=630/1.635=385.32
𝐺𝐶 =
𝑛𝐶
𝑛𝐶′
𝑛𝐶′ = 𝑛𝐶/GC=400/0.639=626
𝑛𝐶′ = 𝑛𝐶/GC=630/0.639=986
n(TH) n(PR)
100 100
160 160
250 244.64
400 385.32
630 626
100 986
Deviated
Speeds

Speed Deviation ∆n
nth 100 160 250 400 630 1000
nact 100 160 244.64 385.32 4 986
∆n 0 0 -2.144 -3.67 -0.639 -1.40
Limit for speed deviations
∆n < ± 10(ɸ-1)٪
∆n < ± 10(1.58-1)=5.8٪
Speed Deviation
Diagram

Difference between number of teeth on
successive gears in change gear box

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•Input speed= 120 RPM
•Draw structure diagram
•Find Spindle speeds.
•Speed trapped for given position
•Speed ratio?
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SPPU Questions

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